I. Diatonic or Chromatic?
How a harp is tuned partly depends on what type of harp you are playing. Most harps are tuned diatonically (like the white keys on a piano), however some multi-course harps (e.g. cross-strung harps) are tuned chromatically. Diatonic harps obtain sharps and flats by the use of levers, blades, hooks or pedals (depending on the style of harp). Chromatic harps are tuned to a chromatic scale, so the sharps and/or flats are built in. For instance, on a cross-strung harp, usually one row of strings is tuned to a diatonic scale, while the other row provides the sharps and/or flats.
An example of a diatonic scale would be: C D E F G A B C
An example of a chromatic scale would be: C C# D D# E F F# G G# A A# B C
For the sake of ease, from this point on I will only refer to "levers" when talking about ways of adding sharps and flats (depending on your type of harp, feel free to mentally substitute "hooks", or "blades" in the case of wire harps); pedal and chromatic harps can play in any key, so the next section does not apply to them.

II. What Key To Tune To? (C major / Modal & Pentatonic / Flat Keys / Sharp Keys)
(If you're wondering, "what's a key?" click here).
There are people who will tell you that one key is "better" or "worse" than another. Like with many harp-related things, it is not so much a matter of right and wrong, but is rather very subjective and individual, and depends on a number of factors, including: what type of harp you have, how much musical experience you have, what style(s) of music you want to play, and how much theory you know. It can even depend on things such as, how much improvising and/or transposing you want to do, and how much you rely on written music (i.e. sheet music). So instead of trying to tell you the "right way" to tune a harp, I've presented some of the more common keys/tunings, with explanations as to why some people choose them and others don't.

(i) Tuning with no flats or sharps - the key of C major (also see "modal tuning" below)
Many lap harps come tuned in the scale of C major. There are a couple of reasons for this. Lap harps (e.g. small harps with 19-25 strings) are less likely to come with a full set of levers. They are also more commonly used by beginners than bigger harps. Most beginner books stick to tunes with simple key signatures (usually C major and A minor, which have no sharps or flats, and possibly keys with one or two sharps at most - see (iii) below). Some people may start out with a harp with no levers, and add them on as they need them (for instance, if they start to play with other people, or aquire a book of music where many of the tunes contain sharps or flats, then they may choose to re-tune their harp and/or add more levers). Some people suggest a C major tuning as a good start for beginners since it is less confusing when you don't have to worry about flipping levers all the time. However, some people come to the harp from a long background of musical experience, and may want to start out right away with a wider variety of keys at their disposal (see other tunings, below). People who are good at improvising or transposing might choose to just keep their harp lever-free, e.g. if they learn by ear. However, people who rely mostly on sheet music, or want to sing with the harp, or want to play in a group, may find the lack of levers (and key variety) restrictive.

(ii) Tuning in flats: F, Bb, Eb and Ab major tunings
Depending on what type of music you play, flat keys can be quite prevalent in harp music. Some older books and tune collections (e.g. "The Small Harp" by Margaret Hewett, see Method Books) may contain quite a few tunes in flat keys. You will also run across a wider variety of keys if you choose to play Classical or Jazz, or even some Pop/Rock and New Age. For instance, I play in a trio that plays Celtic and Classical mainly, and our keys range all the way from Eb major (3 flats) to A major (3 sharps) and occasionally E major (4 sharps). For that reason, and because I also play many other styles of music, I tune my two main (nylon-strung) harps to the key of Eb, because it gives me the most flexibility. Some people will reccommend this because it offers you the maximum number of possible different keys to play in. However, some people may find they don't need an extensive range of keys, for instance if they only play Celtic, folk or early music. Some people choose to only include one or two flats - e.g., if you want to play medieval music, you will likely come across Bb fairly often, but that's about it. My wire harp is tuned to be played modally, with no sharps or flats except Bb (since I come across the Bb so often in medieval music, I've tuned my wire harp thusly: C D E F G A Bb B C). Other flat keys include Bb major (two flats, B and E) and Ab major (four flats).
Some reasons why people choose not to tune with flats are: they find that the strings don't ring quite as true with levers engaged, and/or they only play modal tunes or tunes in sharp keys, or they can't afford to have a full set of levers installed on their harp.

(iii) Tuning in sharps: G and D major
While it's not as common to tune your harp to the scale of G or D major, people who plays lots of Celtic/folk music and/or hymns will find themselves playing in these keys quite often. Frequently people who play mainly in the keys of C, G and D (and their relative minors) will tune their harp to C major, and only add levers on the F's and C's. Since levers can be expensive, this enables you to be frugal and still gives you some variety of keys to choose from. It should also enable you to play through one or two levels of beginner books with no problem (most method books and introductory books stick within these keys). The argument for this tuning is similar to the one for C major without levers (see above) - you can always re-tune your harp (and/or add levers) if you find your changing musical tastes or repertoire require it. My very first harp (a 22-string lap harp) had working levers only on C's and F's, and I played it quite happily for three years before I started to require a wider range of keys. Keep in mind that if you tune your harp to G or D (i.e. your F's and/or C's are tuned to F# and/or C#, with levers disengaged), then you will not be able to play in C major or A minor (this is why people usually tune to C and then add F and C levers to get the sharps).

(iv) Modal and Pentatonic Tuning
All of the old Greek modes can be played on a harp with no levers, tuned to the scale of C major (no flats or sharps). Modes, like any other scales, are simply a pattern of tones and semitones (e.g. if you want to play in Dorian mode, you can start on any note as long as you follow the pattern - so you can play in D Dorian, or G Dorian). For the sake of simplicity, below I've listed the main Greek modes as they would be played on a harp tuned in C:
Ionian (same as "major"): C D E F G A B C
Dorian: D E F G A B C D
Phrygian: E F G A B C D E
Lydian: F G A B C D E F
Myxolydian: G A B C D E F G
Aoelian (also known as "natural minor"): A B C D E F G A
Locrian (rarely used): B C D E F G A B
The old modes listed above can be found in many types of music, from many different centuries. People wanting to play medieval music on the harp will often stick to playing in modes, however many of the modes can also be found in modern music. Dorian and Aeolian, for instance, are quite common in Celtic music (and other folk music), as is Myxolydian.
A pentatonic scale is a five-note, or "gapped" scale, e.g. C D E G A C (like a major C scale, but missing the F and B). A pentatonic tuning is probably the most restrictive in terms of limiting the different kinds of tunes you can play, but may be appropriate if you are exclusively playing one kind of music on that particular instrument. It may also be used on a very small instrument, such as a lyre or miniature harp. Pentatonic tunes are actually quite common, especially in folk and roots music.

One of the more unusual facets of the harp is the vast diversity of range that it can have. Many instruments come in several sizes (e.g. soprano, alto, tenor, bass), from recorders to saxaphones. However, harps are probably the most diverse in terms of all the different sizes they can come in. Harps can have as few as 9 to 19 strings or as many as 47. In terms of highest and lowest note, even on harps with the same number of strings this can vary, depending on the maker. For instance - a lap harp of 22 strings may go down to the C below middle C, or to the G or F below middle C. Larger harps, of 34 strings or more, generally have at least two octaves below middle C. Concert Grand pedal harps have a range of 47 strings, over six octaves in total. "Semi Grand" pedal harps are a bit shorter, with 46-47 strings. There are also "petite" models of pedal harp, with around 40 strings, for people who want more portability and a more manageable size. The larger lever (folk) harps can have as many as 38-40 strings, however the most common ranges for a floor-model lever harp are 34 or 36 strings (five octaves).

Note for Beginners - What Are Keys and Scales, Anyhow?
A "scale", as shown in the examples above, is a particular pattern of notes - more specifically, a particular pattern of tones and semitones (in other words, a pattern of full steps, like the C to D on a piano, and half-steps, like going from a white key to a black key, e.g. going from C to C sharp). If you play a song using only the notes of a particular scale, you are said to be playing in the "key" of that scale (especially if you start and/or end on the root, or first, note of that scale). So if you play only the notes of a C major scale (C D E F G A B C), you are said to be playing in the key of C major. Since most harps are diatonic, that means they are set in a particular scale. For instance, a three-octave harp may be made up of three repetitions of a C scale. That doesn't mean you are only restricted to playing in that scale however; if you use the same notes but starting from a different spot, you can find yourself playing a whole new scale (for instance, if you start on D and play D E F G A B C D) you are playing in the dorian mode (modes are a type of scale; or one might say a scale is a type of mode!). Sound confusing? If you're still puzzled, you will probably want to talk to someone who has some musical theory knowledge before deciding what key you want your harp to be in (see examples of keys above). Consider picking up a basic theory book or talking to a teacher - you may find that a lot of musical jargon will start to make much more sense!